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Manchana Lakshman et al/ International Journal of Biomedical Research 2015; 6(03): 164-171. 164
IJBR (2015) 6 (03) www.ssjournals.com
International Journal of Biomedical Research
ISSN: 0976-9633 (Online); 2455-0566 (Print) Journal DOI: 10.7439/ijbr
CODEN: IJBRFA Original Research Article
Evaluation of sigma metrics in a Medical Biochemistry lab
Manchana Lakshman*1
, B.Ravindra Reddy2, P. Bhulaxmi
1, K. Malathi
1, Mahjabeen Salma
1
and Swati Prakasham1
1Department of Laboratory Medicine, Yashoda Hospital, Somajigda, Hyderabad 500082 Telangana 2Department of Biochemistry, MNR Medical college, Sangareddy, Hyderabad, Telangana.
*Correspondence Info: Dr. Manchana Lakshman,
Consultant Biochemist,
Department of Laboratory medicine,
Yashoda Hospital, Somajigda, Hyderabad. 500082. Telangana
E-mail: [email protected]
Abstract
Sigma metrics is calculated in our lab and evaluated from December 2013 to November 2014. It is
observed that Triglycerides, Lactate, Uric acid, AST, Urea, Creatine kinase(CK), Phosphate, Total Bilirubin are
the best performers and the sigma value is more than 6.0 in both in normal and abnormal levels. Iron and
Creatinine are best performers in normal level and Prolactin and Vitamin B12 are best performers in abnormal
level. Amylase and LDH are the poor performers at level 1 (normal), though they show sigma between 3 to 6 at
level 2 which is clinically acceptable.
Keywords: Six sigma, Sigma metrics, Percentage Bias, Total allowable error, Total analytical error, Coefficient
of variance
1.Introduction
It is the time to improve the quality
accompanied by reduction of cost in healthcare
system of both public and private sectors. This
pressurises to implement Total Quality Management
which includes Quality planning, Quality Laboratory
Process, Quality Control, Quality assessment, Quality
Improvement. Quality refers to satisfaction of the
needs and expectations of the users or customers.
Fundamental requirements for all objective quality
control systems are clearly defined quality goals.
Laboratories must define their service goals and
establish clinical analytical requirements for testing
processes. Without such quality goals, there is no
objective way to determine whether acceptable
quality is being achieved.
Six sigma is an evolution in quality
management that is being widely implemented in
business and industry in the new millennium. The
principles of Six sigma was adopted by Motorola in
early 1990s and won the award of Malcolm
Baldridge Quality Award. The application of sigma
metrics for assessing analytical performance depends
on measuring the process variation and determining
process capability in sigma units. Sigma(σ) is the
mathematical symbol for standard deviation(SD).
Any process can be evaluated in terms of
a sigma metric that describes how many sigma's fit
within the tolerance limits. Two methods can be used
to assess the process performance in terms of a sigma
metric. One approach is to measure outcomes by
inspection. The other approach is to measure
variation and predict process performance.
Measurement of outcome is done by calculating
defects per million(DPM) and converting it into
sigma metric. A defect rate of 0.033% would be
considered excellent in any healthcare organization,
where error rates from 1 to 5% are often considered
acceptable. A 5% error rate corresponds to a 3.15
sigma performance, and a 1% error rate corresponds
to 3.85 sigma. Quality is assessed on the sigma scale
with a criterion of 3 σ as the minimum allowable
sigma for routine performance and a sigma of 6 σ
being the goal for world-class quality.[1] To achieve
Six sigma goal, the error rate should be 0.1% (4.6
Manchana Lakshman et al / Evaluation of sigma metrics in a Medical Biochemistry lab 165
IJBR (2015) 6 (03) www.ssjournals.com
sigma) to 0.01% (5.2 sigma) and ultimately 0.001%
(5.8 sigma).2 We aimed to gauze the sigma values on
sigma metrics scale.
2. Materials and Methods
Six Sigma is unique in its rigorous
approach to outlining the details that are necessary to
achieve significant improvement in process quality
and efficiency. The process begins with developing a
clear understanding of required performance. It then
applies a variety of statistical tools to analyze process
measures, which facilitates proving the root cause(s)
for problem(s). The task then becomes revising the
process in order to eliminate the causative factor(s).
We determined the sigma values for
various parameters and evaluated sigma metrics from
December 2013 to November 2014. Sigma (σ) value
is calculated with the formula Sigma metrics (σ) =
(TEa % - Bias %) / CV% where TEa% is Total
allowable error percentage and CV% is Coefficient of
Variation.
2.1 Precision
Precision has been defined as the closeness
of agreement between independent results of
measurements obtained under stipulated conditions.
The degree of precision is usually expressed on the
basis of statistical measures of imprecision, such as
CV%. CV% is calculated from Internal Quality
Control (IQC) data with the formula CV% =
(SD/Mean)* 100. Monthly CV% of all the analytes
from Dec 2013 to Nov 2014 is shown in Table 1 and
Table 2.
2.2 Trueness
Trueness is defined as closeness of
agreement between the average value obtained from a
large series of results of measurements and the true
value. The difference between the average value and
the true value is the bias, which is expressed
numerically and so is inversely related to the
trueness. Bias% is calculated from External Quality
Assurance Scheme (EQAS) with the formula:
Bias% = [(Our lab result - Peer group mean)
/ (Peer group mean)]*100. Bias% of all the analytes
from Dec 2013 to Nov 2014 is shown in Table 3.
Various parameters observed are Amylase,
ALT, ALKP, AST, Conjugated Bilirubin, Total
Bilirubin, Cholesterol, Creatine kinase, Creatinine,
Glucose, HDL Cholesterol, Iron, Lactate, LDH,
iPTH, Phosphorus, Potassium, Prolactin, PSA,
Triglycerides, Uric acid, Urea, Vitamin B12 . The
analysers used are Vitros 5.1FS, Rochester, U.S.A.
and Advia Centaur CP, Marburg, Germany. Internal
and External Controls are procured from Biorad
Laboratories, Irvine, U.S.A. Internal controls are of
lyophilsed serum materials of different
concentrations one being the physiological/normal
level (Level 1) and the other of pathological
level/abnormal (Level 2).
In our sudy, Total allowable errors (TEa)
for calculating the sigma metrics are taken from the
guidelines of Dr. Carmen Ricos and her
colleagues.[3] TEa for various parameters is as
follows: Amylase-17.5, ALT-32.4, ALKP-13.9,
AST-19.2, Conjugated Bilirubin-57.1, Total
Bilirubin-39.1, Cholesterol-10.3, Creatine kinase-
38.1, Creatinine-11.0, Glucose-9.3, HDL
Cholesterol-13.5, Iron-39.7, Lactate-39.7, LDH-14.3,
iPTH-39.0, Phosphorus-13.1, Potassium-7.4,
Prolactin-37.3, PSA-39.7, Triglycerides-35.0, Uric
acid-15.4, Urea-19.8, Vitamin B12-35.1.[3]
3. Results
Among the 23 analytes observed in Level
1 (normal level) Triglycerides, Lactate, Uricacid,
Iron, AST, Urea, Creatine kinase, Phosphorus,
Prolactin, Total Bilirubin, Creatinine showed the
performance of more than 6 sigma. Cholesterol,
Vitamin B12, Glucose, iPTH, ALKP, Potassium,
PSA, Conjugated Bilirubin, ALT, and HDL
Cholesterol showed 3 – 6 sigma performance. LDH
and Amylase are poor performers (sigma metrics is
less than 3.0) (Table 4) (Figure 1)
In level 2 (pathological level)
Triglycerides, Lactate, Total Bilirubin, ALT, AST,
Urea, Uricacid, Creatine kinase, Phosphorus,
Cholesterol, Vitamin B12 showed the performance of
more than 6 sigma. Prolactin, LDH, ALKP, Amylase,
Creatinine, Glucose, PSA, iPTH, Conjugated
Bilirubin, Iron, HDL Cholesterol, and Potassium
showed the performance between 3 and 6. (Table 5)
(Figure 2)
4. Discussion
In a routine accredited clinical
biochemistry laboratory it is conventional practice to
run the Internal and External quality controls to
assess precision and accuracy. In this practice,
laboratory personnel usually follow the Westgard
rules like 12S, 13S, R4S, and 10X for internal quality
assurance.
Rule 12S indicates one control observation
exceeding the mean ± 2 standard deviations is used as
a warning rule that intiates testing of the control data
by the other control rules.
Rule 13S indicates one control observation
exceeding the mean ± 3 standard deviations is
rejection rule that is primarily sensitive to a random
error,
Manchana Lakshman et al / Evaluation of sigma metrics in a Medical Biochemistry lab 166
IJBR (2015) 6 (03) www.ssjournals.com
Rule 22S indicates two control
observations exceeding the same mean plus 2
standard deviations or minus 2 standard deviations
limit is rejection rule that is sensitive to systematic
error.
Rule R4S indicates one observation
exceeding the mean plus 2 standard deviation and the
other exceeding the mean minus 2 standard deviation
is a rejection rule that is sensitive to random error.
Rule 10 x indicates ten consecutive control
observations falling one side of the mean is a
rejection rule that is sensitive to systematic error.[2]
Common checklist followed when a systemic error
is noted includes:
1. Change in the Reagent/Control/ numbers.
1. Weekly / monthly maintenance due.
2. Date and Time of current calibration.
3. Calibrator lot change.
4. Any maintenance / Service done since the shift
/trend is noted.
5. Any lamp change / lamp deterioration.
6. Reagent shelf / on board stability.
7. Date of reconstitution of the control.
8. Status after repetition of control.
9. Correlation of lab Mean and SD with peer group
Mean and SD.
Common checklist for corrective action when a
random error is noted includes:
1. Proper mixing of the control.
2. Any bubbles noted in aliquot.
3. Shelf life of reconstituted control.
4. Temperature/humidity of environment and
instrument.
5. Calibration status.
6. Electricity fluctuation.
7. Reagent/control/calibrator lot change.
8. Any instrument error.
9. Status after repetition of the control.
In External Quality Assurance Services
(EQAS) when ' Z ' score (or) Standard Deviation
Index (SDI) is between +2 and -2, it is considered as
accuracy is satisfactory. If Z-score is out of this
range it indicates the process is biased.When the
process is biased the frequent corrective actions
include calibrating the parmeter, Reagent change,
Maintenance of intrument, EQAS sample handling,
technician change, sending the sample for Inter
Laboratoty Comparison, EQAS evaluation.
Internal Quality Control (IQC)
programme can proffer CV% which represents
laboratory precision and EQAS can provide Bias%
representing the accuracy.
Total error (TE) = 1.96 * CV% + Bias %.
CV% can be calculated from the internal quality
control and Bias percentages can be known from
EQAS results. So, it is clear that calculation of total
error takes into the consideration of both precision
and accuracy. From this it appears that if Total error
(TE) is less than Total allowable error (TEa), we can
cosider the process satisfactory. But it is not so
because other factors like sample carry over, non
linear bias and sample matrix effects can also affect
the Total analytical error.[4]
Total analytical error
(TE) for observed analytes from Dec 2013 to Nov
2014 is showed in Table 6 and Table 7.
Total allowable errors (TEa) for different
analytes are published by different groups like
Clinical Laboratory Improvement Amendments
(CLIA), Royal College of Australasian Pathologists
(RCPA), as well as the Guidelines of the German
Medical Association (RiliBäk). Dr. Carmen Ricos
and her colleagues have provided a continuously
updated database of biologic variation since 2000.
For over 300 different analytes, they have tabulated
desirable specifications for imprecision, inaccuracy,
and total allowable error.[5]
The Six Sigma scale typically runs from
zero to six, but a process can actually exceed Six
Sigma, if variability is sufficiently low as to decrease
the defect rate. In industries outside of healthcare, 3
Sigma is considered the minimal acceptable
performance for a process. When performance falls
below 3 Sigma, the process is considered to be
essentially unstable and unacceptable.[5]
In contrast to other industries, healthcare
and clinical laboratories appear to be operating in a 2
to 3 Sigma environment. The routine use of “2s” (i.e.,
2 standard deviations or 2 SD) control limits is
indicative of a complacent tradition in quality control
practices. Despite the well-known problems of 2s
limits – they can generate false rejection rates of up
to 10 to 20%, depending on the number of controls
run– many laboratories use them for all testing
processes. The misuse of 2s limits in laboratory
testing frequently results in erroneously-repeated
controls, excessive trouble-shooting, or worse still,
workarounds that artificially widen control limits to
the point that laboratories can no longer detect
critical analytical errors.
Six sigma scale has the power to provide a
universal bench mark. It allows the comparison
between different instruments, different labs and
different methods all over the world. Nevalainen’s
data on Sigma assessment in preanalytic, analytic and
post analytic phases of the clinical lab showed that
many were not adequate.[6] Nanda et al data showed
that out of the 13 analytes evaluated for sigma
assessment in their laboratory, 5 analytes showed the
Manchana Lakshman et al / Evaluation of sigma metrics in a Medical Biochemistry lab 167
IJBR (2015) 6 (03) www.ssjournals.com
performance of above 6 sigma, 4 analytes showed the
performance between 3 to 6 sigma metrics and
remaining 4 showed the performance of below 3
sigma metrics.[7] Singh et al data showed that among
the 15 analytes observed for sigma assessment three
analytes showed the performance of below 3 sigma
metrics.[8]
In present study, 11 of 23 analytes showed
above six sigma performances, 10 analytes showed 3
to 6 sigma performance, 2 analytes showed less than
3 sigma performances in normal level (level 1).
Sigma metrics of abnormal level (level 2) showed 11
of 23 analytes showed above six sigma
performances, 12 analytes showed the performance
between 3 and 6.
Though many laboratories are following the
ISO 15189 guidelines and participating in the Internal
and external quality control programmes, unable to
achieve the six sigma performance. Six sigma being
the goal for world-class quality, there is a need to
implement the sigma metrics in the laboratories.
Sigma metrics in combination with a rational QC
design for each analyte can improve the quality there
by reducing the wastage. [5]
Schoenmaker et al described the importance
of application of sigma metrics and preparation of
rational QC design based on the sigma values with
the help of westgard operational specifications chart
(OPSpecs chart) in clinical biochemistry
laboratories.[9] An example of QC design is shown in
the Table 8.
Table 1: Coefficient of Variance (CV %) Level 1 Monthly wise Dec 2013 – Nov 2014
Analyte
Dec
2013
Jan
2014
Feb
2014
March
2014
April
2014
May
2014
June
2014
July
2014
Aug
2014
Sep
2014
Oct
2014
Nov
2014
AVG
CV%
Amylase 6.5 5.72 3.36 5.22 5.66 5.09 5.09 6 7.9 5.12 6.44 3.87 5.4
ALT 7.89 8.15 6.52 8 8.09 9.53 9.53 10.43 11.18 7.42 6.2 10.37 8.6
ALKP 1.89 1.85 2.24 3.5 2.8 2.02 2.02 2.1 2.65 4.38 2.2 2.16 2.4
AST 2.26 2.03 2.13 2.63 1.94 1.65 1.65 1.44 1.86 1.3 1.81 1.78 1.8
Conjugated bilirubin 12.5 8.6 9.9 12.7 10.5 13 13 8.5 8 14.9 13.1 7.7 11.0
Total Bilirubin 2.97 4.98 3.58 4.18 5.61 5.05 5.05 5.27 5.32 5.81 6.55 4.6 4.9
Cholesterol 0.89 1.74 0.93 1.89 1.14 1.59 1.59 1.94 1.73 1.65 1.01 1.5 1.4
CreatineKinase (CK) 4.7 7.43 4.94 5.24 3.57 3.33 3.33 5.49 4.78 3.19 3.02 3.45 4.3
Creatinine 1.52 1.76 1.43 2.37 1.46 1.24 1.24 0.99 1.31 1.09 1.07 1.4 1.4
Glucose 1.02 1.32 0.99 3.56 1.06 0.99 1.26 1.19 2.46 1.74 1.07 0.99 1.4
HDL Cholesterol 2.8 1.88 2.26 3.3 2.99 3.63 4.72 3.19 4.22 3.3 3.49 4.08 3.3
Iron 3.86 3.29 3.65 4.07 2.89 2.29 2.35 2.95 4.52 4.51 4.42 4.11 3.5
Lactate 0.97 1.44 1.79 3.09 3.01 1.56 1.61 0.93 0.71 1 1.32 0.94 1.5
LDH 4.83 4.21 4.02 6.15 5.13 4.83 3.63 4.88 3.44 3.73 4.18 4.17 4.4
iPTH 5.1 10.29 6.26 4.63 7.83 8.79 2.84 6.96 5.84 7.18 13.38 12.03 7.5
Phosphate 0.96 2.7 0.61 1.24 1.01 1.41 1.29 0.99 1.76 2.77 0.74 1.04 1.3
Potassium 0.96 1.73 1.15 0.94 0.62 0.84 5.99 0.52 1.67 2.92 1.3 1.51 1.6
Prolactin 1.12 5.03 6.19 9.18 9.04 7.06 8.32 5.2 3.9 1.62 7.57 4.09 5.6
PSA 9.04 3.69 7.92 6.78 4.21 6.67 2.14 11.68 7.92 11.89 13.89 11.4 8.1
Triglycerides 1.06 1.65 0.93 1.09 1.09 1.07 0.92 0.89 1.69 1.24 1.46 0.84 1.1
Uric acid 0.86 1 0.92 2.54 1.15 1.09 1.34 1.53 1.09 1.17 1.13 0.92 1.2
Urea 1.91 2.25 1.35 2.41 1.8 1.71 1.97 1.55 1.61 2.02 1.48 1.9 1.8
Vitamin B12 5.07 5.17 5.36 12.63 8.23 9.4 6.69 2.67 7.84 2.5 5.14 7.07 6.4
Table 2: Coefficient of Variance (CV %) Level 2 Monthly wise Dec 2013 – Nov 2014
Analyte
Dec
2013
Jan
2014
Feb
2014
March
2014
April
2014
May
2014
June
2014
July
2014
Aug
2014
Sep
2014
Oct
2014
Nov
2014
AVG
CV%
Amylase 2.28 3.85 1.31 1.84 2.19 3.08 2.67 1.8 2.21 3 4.27 1.8 2.5
ALT 2.53 2.52 3.12 3.44 2.34 1.73 2.96 3.31 2.68 2.79 1.91 2.07 2.6
ALKP 2.09 2.03 1.68 3.12 1.35 1.94 1.87 1.59 1.81 2.79 1.95 2.14 2.0
AST 1.72 1.65 2.27 2.27 1.7 1.7 1.05 1.77 1.32 1.37 1.34 1.66 1.6
Conjugated bilirubin 6.93 7.5 5.95 7.58 6.2 7.98 8.01 12.62 8.95 7.46 11.45 8.39 8.2
Total Bilirubin 1.25 3.06 2.33 2.48 1.91 2.13 1.76 2.15 2.69 4.26 1.54 1.26 2.2
Cholesterol 0.96 3.2 1.05 0.95 0.97 0.96 1.38 1.37 1.43 1.86 0.74 0.85 1.3
Creatine kinase (CK) 7 7.95 6.22 9.88 3.18 3.13 3.78 2.47 3.02 2.22 2.64 2.59 4.5
Creatinine 1.32 1.97 2.24 2.05 2.01 1.64 1.75 2.41 1.18 1.66 1.43 1.32 1.7
Glucose 1.05 1.95 1.36 1.48 1.09 1.33 1.21 1.32 1.79 2.12 1.49 0.94 1.4
HDL Cholesterol 2.83 1.32 1.74 2.61 2.19 2.69 2.54 1.56 2.87 3.05 2.58 2.02 2.3
Iron 6.62 4.45 8.54 6.95 6.66 5.6 8.95 10.46 9.77 7.2 10.75 11.44 8.1
Lactate 2.25 2.64 2.39 3.94 2.61 1.6 2.06 1.68 1.91 2.02 1.54 2.73 2.2
LDH 2.84 1.57 2.09 1.77 1.74 1.62 1.66 1.73 1.87 1.4 1.59 1.37 1.7
iPTH 11.7 2.27 3.78 7.96 9.56 9.97 12.8 7.54 13.08 6.45 8.02 3.14 8.0
Phosphate 1.45 2.21 0.86 1.67 0.83 1.24 2.04 0.92 1.02 2 0.74 0.91 1.3
Potassium 0.88 3.45 1.25 0.86 1.09 1.18 0.87 0.62 1.98 2.94 1.03 1.4 1.4
Prolactin 7.14 1.63 8.92 5.46 3.56 8.51 6.67 3.18 4 4.67 5.99 8.44 5.6
PSA 8.59 1.42 8.52 8.69 8.82 5.79 11.5 10.25 11.14 9.87 11.53 7.36 8.6
Triglycerides 1.1 3.54 0.78 1.02 2.56 1.24 1.26 1.46 1.67 2.17 1.08 1.3 1.5
Uric acid 1.13 1.72 1.23 2.53 2.2 1.55 1.15 1.26 0.99 1.59 1.26 0.98 1.4
Urea 1.33 1.82 1.67 1.75 1.19 1.25 1.27 2.24 2.06 2.08 1.67 1.52 1.6
Vitamin B12 4.19 4.17 5.37 5.41 1.44 7.01 6.82 5.65 6.18 7.52 5.71 5.77 5.4
Manchana Lakshman et al / Evaluation of sigma metrics in a Medical Biochemistry lab 168
IJBR (2015) 6 (03) www.ssjournals.com
Table 3: BIAS % Monthly wise Dec 2013 – Nov 2014
Analyte Dec
2013
Jan
2014
Feb
2014
March
2014
April
2014
May
2014
June
2014
July
2014
Aug
2014
Sep
2014
Oct
2014
Nov
2014
AVG
Bias%
Amylase 6.13 12.5 0.3 0.7 16.1 7.28 4.24 3.46 6.29 6.38 0.95 9.06 6.1
ALT 24.6 1.72 1.94 13.5 3.03 2.46 6.78 7.22 6.24 0.71 6.06 0.668 6.2
ALKP 0.133 5.54 7.82 1.17 1.12 6.72 3.28 2.19 2.78 0.3 2.38 1.46 2.9
AST 2.69 1.55 1.91 0.57 0.782 0.3 1.36 2.33 4.83 5.63 2.77 5.96 2.5
Conjugated bilirubin 17.2 15.3 25.7 8.01 0.268 36.5 47.2 16.8 0.43 41.3 23.7 11.9 20.3
Total Bilirubin 1.41 0.19 1.07 6.11 12.7 8.42 5.56 5.67 7.23 0.45 11.4 22.5 6.8
Cholesterol 1.98 2.09 1.12 5.92 0.519 1.86 0.86 2.81 0.98 2.42 3.74 3.51 2.3
Creatine kinase (CK) 0.165 0.1 3.42 4.26 0.918 1.85 6.53 0.44 6.55 0.98 4.7 2.26 2.6
Creatinine 0.173 2.54 2.58 1.72 5.15 2.57 0.5 1.11 1.49 2.81 3.73 4.39 2.3
Glucose 6.55 1.58 0.339 0.35 0.257 1.74 3.78 0.912 2.89 2.88 2.31 6.44 2.5
HDL Cholesterol 5.31 2.53 4.32 7.18 5.95 1.08 1.97 0.603 4.87 7.41 2.08 3.97 3.9
Iron 5.04 2.99 2.13 6.04 13 1.66 7.52 6.84 4.13 6.2 2.06 14.3 5.9
Lactate 0.702 3.1 1.01 8.68 0.472 0.136 0.55 0.48 3.67 4.79 1.63 3.13 2.3
LDH 5.74 3.67 1.39 7.18 2.27 7.86 5.11 3.73 2.32 4.5 1.72 4.1 4.1
iPTH 5.33 10.3 3.42 2.71 5.47 0.24 1.09 0.3 3.96 10.9 3.2 3.9
Phosphate 2.7 12.7 3.16 4.23 7.83 0.3 4.05 0.965 0.753 0.56 4.25 2.69 3.6
Potassium 1.29 11.2 6.8 2.37 7.75 4.05 0.098 0.235 0.23 2.13 1.09 0.189 3.1
Prolactin 16.3 3.37 1.19 0.83 7.65 0.723 0.8 13.5 13.8 5.29 4.99 2.44 5.9
PSA 9.79 10.5 17.1 10.5 7.11 0.32 0.23 18.8 7.39 1.83 5.48 7.9 8.0
Triglycerides 0.06 8.13 0.5 2.19 1.28 2.47 0.22 0.428 4.1 1.67 0.19 8.05 2.4
Uric acid 2.45 0.58 1.96 0.14 0.293 0.478 1.05 1.98 0.77 0.27 1.71 5.04 1.3
Urea 4.32 6.23 1.09 2.59 5.19 2.59 2.34 2.23 2.86 0.17 11.9 0.667 3.5
Vitamin B12 0.618 1.52 8.15 3.97 2.45 19.5 1.83 4.57 6.09 1.82 5.95 1.77 4.8
Table 4: Sigma Metrics Level 1 (Monthly wise Dec 2013 – Nov 2014)
Analyte Dec
2013
Jan
2014
Feb
2014
Mar
2014
Apr
2014
May
2014
Jun
2014
Jul
2014
Aug
2014
Sep
2014
Oct
2014
Nov
2014 AVG Sigma
Triglycerides 33 16.3 37.1 30.1 30.9 30.4 37.8 38.8 18.3 26.9 23.8 32.1 29.6
Lactate 40.2 25.4 21.6 10 13 25.4 24.3 42.2 50.7 34.9 28.8 38.9 29.6
Uric acid 15.1 14.8 14.6 6 13.1 13.7 10.7 8.8 13.4 12.9 12.1 11.3 12.2
Iron 9 11.2 10.3 8.3 9.2 16.6 13.7 11.1 7.9 7.4 8.5 6.2 9.9
AST 7.3 8.7 8.1 7.1 9.5 11.5 10.8 11.7 7.7 10.4 9.1 7.4 9.1
Urea 8.1 6 13.9 7.1 8.1 10.1 8.9 11.3 10.5 9.7 5.3 10.1 9.0
Creatinekinase(CK) 8.1 5.1 7 6.5 10.4 10.9 9.5 6.9 6.6 11.6 11.1 10.4 8.6
Phosphate 10.8 0.1 16.3 7.2 5.2 9.1 2.6 12.3 7 4.5 12 10 8.0
Prolactin 18.8 6.7 5.8 4 3.3 5.2 4.7 4.6 6 19.8 4.3 8.5 7.6
Total Bilirubin 12.7 7.8 10.6 7.9 4.7 6.1 6.6 6.3 6 6.7 4.2 3.6 6.9
Creatinine 7.1 4.8 5.9 3.9 4 6.8 8.5 10 7.3 7.5 6.8 4.7 6.4
Cholesterol 9.3 4.7 9.9 2.3 8.6 5.3 5.9 3.9 5.4 4.8 6.5 4.5 5.9
Vitamin B12 6.8 6.5 5 2.5 4 1.7 5 11.4 3.7 13.3 5.7 4.7 5.8
Glucose 2.7 5.8 6.8 2.5 8.5 7.6 4.4 7 2.6 3.7 6.5 2.9 5.0
iPTH 6.6 3.8 4.6 7.7 4.6 3.8 4.5 5.4 6.6 4.9 2.1 3 4.8
ALKP 7.3 4.5 2.7 3.6 4.6 3.6 5.3 5.6 4.2 3.1 5.2 5.8 4.6
Potassium 6.4 -2.2 0.5 5.4 -0.6 4 6.2 13.8 4.3 1.8 4.9 4.8 4.1
PSA 3.3 7.9 2.9 4.3 7.7 5.9 1.9 1.8 4.1 3.2 2.5 2.8 4.0
Conjugated bilirubin 3.2 4.9 3.2 3.9 5.4 1.6 0.8 4.7 7.1 1.1 2.5 5.9 3.6
ALT 1 3.8 4.7 2.4 3.6 3.1 2.7 2.4 2.3 4.3 4.2 3.1 3.1
HDL Cholesterol 2.9 5.8 4.1 1.9 2.5 3.4 2.4 4 2 1.8 3.3 2.3 3.0
LDH 1.8 2.5 3.2 1.2 2.3 1.3 2.5 2.2 3.5 2.6 3 2.4 2.3
Amylase 1.7 0.9 5.1 3.2 0.2 2 2.6 2.3 1.4 2.2 2.6 2.2 2.2
Figure1: Graph showing Sigma Metrics Level - 1 (Dec 2013 to Nov 2014)
29.6 29.6
12.2
9.99.1 9 8.6 8 7.6 6.9 6.4 5.9 5.8
5 4.8 4.6 4.1 4 3.6 3.1 3 2.3 2.2
0
5
10
15
20
25
30
35
Sigma Metrics Level - 1
Dec 2013 to Nov 2014
Manchana Lakshman et al / Evaluation of sigma metrics in a Medical Biochemistry lab 169
IJBR (2015) 6 (03) www.ssjournals.com
Table 5: Sigma Metrics Level – 2 (Monthly wise Dec 2013 – Nov 2014)
Analyte Dec
2013
Jan
2014
Feb
2014
Mar
2014
Apr
2014
May
2014
Jun
2014
Jul
2014
Aug
2014
Sep
2014
Oct
2014
Nov
2014 AVG Sigma
Triglycerides 31.8 7.6 44.2 32.2 13.2 26.2 27.6 23.7 18.5 15.4 32.2 20.7 24.4
Lactate 17.3 13.9 16.2 7.9 15 24.7 19 23.3 18.9 17.3 24.7 13.4 17.6
Total Bilirubin 30.2 12.7 16.3 13.3 13.8 14.4 19.1 15.5 11.8 9.1 18 13.2 15.6
ALT 3.1 12.2 9.8 5.5 12.6 17.3 8.7 7.6 9.8 11.4 13.8 15.3 10.5
AST 9.6 10.7 7.6 8.2 10.8 11.1 17 9.5 10.9 9.9 12.3 8 10.4
Urea 11.6 7.5 11.2 9.8 12.3 13.8 13.7 7.8 8.2 9.4 4.7 12.6 10.2
Uric acid 11.5 8.6 10.9 6 6.9 9.6 12.5 10.7 14.8 9.5 10.9 10.6 10.2
Creatine kinase(CK) 5.4 4.8 5.6 3.4 11.7 11.6 8.4 15.2 10.4 16.7 12.7 13.8 9.9
Phosphate 7.2 0.2 11.6 5.3 6.3 10.3 4.4 13.2 12.1 6.3 12 11.4 8.3
Cholesterol 8.7 2.6 8.7 4.6 10.1 8.8 6.8 5.5 6.5 4.2 8.9 8 6.9
Vitamin B12 8.2 8.1 5 5.8 22.7 2.2 4.9 5.4 4.7 4.4 5.1 5.8 6.8
Prolactin 2.9 9.8 4 6.7 8.3 4.3 5.5 7.5 5.9 6.9 5.4 4.1 5.9
LDH 3 6.8 6.2 4 6.9 4 5.5 6.1 6.4 7 7.9 7.4 5.9
ALKP 6.6 4.1 3.6 4.1 9.5 3.7 5.7 7.4 6.1 4.9 5.9 5.8 5.6
Amylase 5 1.3 13.1 9.1 0.6 3.3 5 7.8 5.1 3.7 3.9 4.7 5.2
Creatinine 8.2 4.3 3.8 4.5 2.9 5.1 6 4.1 8.1 4.9 5.1 5 5.1
Glucose 2.6 4 5 6 8.3 5.7 6.2 6.4 3.6 3 4.7 3 4.8
PSA 3.5 17.9 2.7 3.4 3.7 6.8 3.4 2 2.9 3.8 3 4.3 4.7
iPTH 2.9 3.8 7.6 4.5 3.8 3.4 3 5 3 5.4 3.5 11.4 4.7
Conjugated Billirubin 5.8 5.6 5.3 6.5 9.2 2.6 1.2 3.2 6.3 2.1 2.9 5.4 4.6
Iron 5.2 8.2 4.4 4.8 4 6.8 3.6 3.1 3.6 4.7 3.5 2.2 4.5
HDL Cholesterol 2.9 8.3 5.3 2.4 3.4 4.6 4.5 8.3 3 2 4.4 4.7 4.4
Potassium 6.9 -1.7 0.5 5.8 -0.3 2.8 8.4 11.6 3.6 1.8 6.1 5.2 4.2
Figure 2: Graph showing Sigma Metrics Level - 2 (Dec 2013 to Nov 2014)
Table 6: Total Analytical Error Level – 1 (Monthly wise Dec 2013 – Nov 2014)
Analyte Dec
2013
Jan
2014
Feb
2014
March
2014
April
2014
May
2014
June
2014
July
2014
Aug
2014
Sep
2014
Oct
2014
Nov
2014
Amylase 19 23.8 6.9528 11.0356 27.3068 17.3582 14.3182 15.34 21.932 16.5176 13.7012 16.7
ALT 40.2222 17.9 14.8496 29.34 19.0482 21.3294 25.6494 27.8714 28.3764 15.4016 18.336 21.2
ALKP 3.8752 9.2 12.2552 8.1 6.664 10.7196 7.2796 6.348 8.027 8.9724 6.736 5.7
AST 7.1648 5.6 6.1274 5.7774 4.6232 3.567 4.627 5.1812 8.5128 8.204 6.3538 9.4
Conjugated bilirubin 41.95 32.3 45.302 33.156 21.058 62.24 72.94 33.63 16.27 70.802 49.638 27.1
Total Bilirubin 7.2906 10.1 8.1584 14.3864 23.8078 18.419 15.559 16.1046 17.7636 11.9538 24.369 31.6
Cholesterol 3.7422 5.5 2.9614 9.6622 2.7762 5.0082 4.0082 6.6512 4.4054 5.687 5.7398 6.4
Creatine kinase (CK) 9.471 14.8 13.2012 14.6352 7.9866 8.4434 13.1234 11.3102 16.0144 7.2962 10.6796 9.0
Creatinine 3.1826 6.0 5.4114 6.4126 8.0408 5.0252 2.9552 3.0702 4.0838 4.9682 5.8486 7.1
Glucose 8.5696 4.2 2.2992 7.3988 2.3558 3.7002 6.2748 3.2682 7.7608 6.3252 4.4286 8.4
HDL Cholesterol 10.854 6.3 8.7948 13.714 11.8702 8.2674 11.3156 6.9192 13.2256 13.944 8.9902 12.0
Iron 12.6828 9.5 9.357 14.0986 18.7222 6.1942 12.173 12.681 13.0796 15.1298 10.8116 22.4
Lactate 2.6226 6.0 4.5542 14.7982 6.4318 3.2248 3.7378 2.3214 5.0758 6.77 4.2436 4.9
LDH 15.3034 12.0 9.3496 19.357 12.4274 17.4234 12.2974 13.3924 9.1312 11.8854 9.9964 12.3
iPTH 15.428 20.4 22.6948 12.5874 18.2134 22.8742 5.8632 14.8708 11.8632 18.1764 37.3924 27.0
Phosphate 4.6008 18.0 4.3678 6.6852 9.8298 3.0918 6.6042 2.9252 4.2378 6.0446 5.7152 4.7
Potassium 3.1908 14.6 9.077 4.2312 8.9776 5.7132 11.9582 1.2646 3.5366 7.9116 3.664 3.1
Prolactin 18.5176 13.3 13.4462 19.0064 25.5492 14.7018 17.2736 23.796 21.522 8.4976 19.9786 10.5
PSA 27.6892 17.8 32.7816 23.9244 15.4458 13.5266 4.4672 41.9264 23.0716 25.3722 32.9822 30.4
Triglycerides 2.1588 11.4 2.3414 4.3482 3.4382 4.5886 2.0416 2.1902 7.4462 4.1252 3.0808 9.7
Uric acid 4.1528 2.6 3.7816 5.1692 2.57 2.6362 3.7032 5.0094 2.9282 2.5866 3.9474 6.8
Urea 8.1018 10.7 3.763 7.3618 8.754 5.9758 6.2406 5.299 6.0478 4.1696 14.8304 4.4
Vitamin B12 10.6566 11.8 18.7628 28.9774 18.7454 38.112 15.0762 9.8566 21.6132 6.77 16.1272 15.7
24.4
17.6
15.6
10.5 10.4 10.2 10.2 9.9
8.36.9 6.8
5.9 5.9 5.6 5.2 5.1 4.8 4.7 4.7 4.6 4.5 4.4 4.2
0
5
10
15
20
25
30Sigma Metrics Level - 2
Dec 2013 to Nov 2014
Manchana Lakshman et al / Evaluation of sigma metrics in a Medical Biochemistry lab 170
IJBR (2015) 6 (03) www.ssjournals.com
Table 7: Total Analytical Error Level – 2 (Monthly wise Dec 2013 – Nov 2014)
Analyte Dec
2013
Jan
2014
Feb
2014
March
2014
April
2014
May
2014
June
2014
July
2014
Aug
2014
Sep
2014
Oct
2014
Nov
2014
Amylase 10.6444 20.123 2.8938 4.3432 20.4362 13.3784 9.5266 7.024 10.6658 12.32 9.4046 12.624
ALT 29.6094 6.7096 8.1176 20.3112 7.6632 5.8854 12.6408 13.7738 11.5464 6.2342 9.8418 4.7666
ALKP 4.2712 9.5594 11.1464 7.3476 3.793 10.5612 6.9826 5.3382 6.3638 5.8242 6.241 5.6972
AST 6.0956 4.817 6.4046 5.0646 4.148 3.666 3.439 5.8346 7.4436 8.3426 5.4232 9.2468
Conju. bilirubin 30.9214 30.15 37.481 23.0184 12.544 52.3004 63.0598 41.7876 18.151 56.0708 46.371 28.5122
Total Bilirubin 3.885 6.2488 5.6834 11.0204 16.4818 12.6374 9.0448 9.927 12.5562 8.8848 14.4492 24.9948
Cholesterol 3.8808 8.426 3.199 7.801 2.4396 3.7608 3.5924 5.5226 3.8114 6.1028 5.2052 5.193
Creatine kinase 14.025 15.841 15.7356 23.8224 7.2144 8.0474 14.0144 5.3306 12.5296 5.3756 9.9272 7.3882
Creatinine 2.7866 6.4406 7.0152 5.779 9.1298 5.8172 3.965 5.8818 3.8264 6.0968 6.5614 7.0036
Glucose 8.629 5.441 3.0318 3.2804 2.4152 4.3734 6.1758 3.5256 6.4342 7.0776 5.2602 8.3012
HDL Cholesterol 10.9134 5.1436 7.7652 12.3478 10.2862 6.4062 6.9992 3.6918 10.5526 13.449 7.1884 7.9696
Iron 18.1476 11.801 19.0392 19.801 26.1868 12.748 25.241 27.5508 23.4746 20.456 23.345 36.9512
Lactate 5.157 8.3272 5.7422 16.4812 5.6398 3.304 4.6288 3.8064 7.4518 8.7896 4.6792 8.5354
LDH 11.3632 6.7786 5.5282 10.6846 5.7152 11.0676 8.3968 7.1554 6.0226 7.272 4.8682 6.8126
iPTH 28.496 17.1946 17.7844 19.1808 21.6388 25.2106 25.584 16.0192 26.1984 16.731 26.7796 9.4172
Phosphate 5.571 15.5758 4.8628 7.5366 9.4734 2.7552 8.0892 2.7866 2.7726 4.52 5.7152 4.4918
Potassium 3.0324 10.201 9.275 4.0728 9.9082 6.3864 1.8206 1.4626 4.1504 7.9512 3.1294 2.961
Prolactin 30.4372 13.7274 18.8516 11.6408 14.6988 17.5728 14.0066 19.7964 21.72 14.5366 16.8502 19.1512
PSA 26.7982 5.0316 33.9696 27.7062 24.5736 11.7842 23 39.095 29.4472 21.3726 28.3094 22.4728
Triglycerides 2.238 15.1392 2.0444 4.2096 6.3488 4.9252 2.7148 3.3188 7.4066 5.9666 2.3284 10.624
Uric acid 4.6874 3.9856 4.3954 5.1494 4.649 3.547 3.327 4.4748 2.7302 3.4182 4.2048 6.9804
Urea 6.9534 9.8336 4.3966 6.055 7.5462 5.065 4.8546 6.6652 6.9388 4.2884 15.2066 3.6766
Vitamin B12 8.9142 9.7766 18.7826 14.6818 5.3012 33.3798 15.3336 15.757 18.3264 16.7096 17.2558 13.1946
Table 8: Example of A QC design based on sigma metrics
Sigma Westgard Rule Levels Measurements P Error Detection P False Rejection
6.0 1 3.5s 2 1 0.98 0.01
5.8 1 3.5s 2 1 0.98 0.00
5.6 1 3s 2 1 0.97 0.00
5.4 1 3s 2 1 0.94 0.00
5.2 1 3s 2 1 0.91 0.00
5.0 1 2.5s 2 1 0.96 0.03
4.8 1 2.5s 2 1 0.93 0.03
4.6 1 3s 2 1 0.92 0.01
4.4 1 2.5s 2 1 0.96 0.04
4.2 1 2.5s 2 1 0.92 0.04
4.0 1 3s/2 2s/R 4s/4 1s 2 2 0.91 0.03
3.8 1 3s/2 2s/R 4s/4 1s 2 2 0.86 0.03
3.6 1 3s/2 2s/R 4s/4 1s 2 2 0.79 0.03
3.4 1 3s/2 2s/R 4s/4 1s 2 2 0.65 0.03
3.2 1 3s/2 2s/R 4s/4 1s 3 2 0.48 0.03
3.0 1 3s/2 2s/R 4s/4 1s 3 2 0.36 0.02
5. Conclusion
Out of 23 analytes evaluated for six sigma
assessment 11 parameters that is Lactate,
Triglycerides, Uric acid, Iron, AST, Urea, Creatinine
kinase, Phosphate, Prolactin, Total Bilirubin,
Creatinine showed the sigma value of more than 6.0,
Cholesterol, Vitamin B12, Glucose, iPTH, ALKP,
PSA, Potassium, Conjugated bilirubin, ALT, HDL
Cholesterol showed the performance between 3 and 6
and LDH, Amylase showed the performance below
3.0 in level 1. Sigma scale on level 2 showed
Triglycerides, Lactate, Total Bilirubin, ALT, AST,
Uric acid, Urea, Creatinine kinase, Phosphate,
Cholesterol, Vitamin B12 with the performance of
above six sigma and Prolactin, LDH, ALKP,
Amylase, Creatinine, Glucose, Conjugated bilirubin,
PSA, iPTH, Iron, HDL Cholesterol, Potassium with
the performance between 3 and 6. So it is the need of
the hour to implement the Sigma metrics with the
help of IQC and EQAS and combining Sigma metrics
with QC Design tools, such as the Operating
Specifications chart (OPSpecs), allows the laboratory
to customize and optimize the QC procedures. A
rational QC Design can eliminate much of the
wasteful 2s QC practices, replacing them instead with
appropriate control limits and numbers of control
measurements.
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